This thesis describes the use of a multi-amplitude minimum shift keying (MAMSK) signal in various types of wireless communication system. A MAMSK signal is a bandwidth efficient modulation scheme obtained by superimposing ℳ minimum shift keying (MSK) signals with unequal amplitudes. The overall phase of a MAMSK signal is controlled by the phase of the largest component MSK signal which allows the use of a low-complexity differential detector. A closed form expression for the average bit error rate (BER) for coherent detection of an MAMSK in AWGN is derived and is shown to achieve the same BER as that of square constellation quadrature amplitude modulation (QAM) with the same average transmit power. We describe the design and implementation of a STBC-based MIMO radio system in conjunction with MAMSK modulation. The proposed system provides high capacity data transmission by carrying information not only in the phases but also in the amplitude. Despite using a simple MAMSK differential receiver the system achieves performance within 1 dB of coherent detection. The existing MSK modems in conjunction with STBC could easily be modified to construct the proposed system. The MAMSK modulation scheme is extended to a multiuser relaying network where two nodes cooperate in a half-duplex environment to achieve diversity gain. The cooperative scheme is based on superposition modulation using a decode-and-forward (DF) strategy. In the proposed scheme, each node simultaneously transmits its own and the relayed signals by superimposing one on the other. A MAMSK signal is an excellent choice for this type of cooperative communication due its being obtained by a superposition technique. The proposed system exploits the overall phase of a MAMSK signal which allows differential detection and as a result it provides the lowest decoding complexity and memory requirements among the existing superposition based cooperation schemes. The performance of the system is evaluated by simulation, where it is shown that the MAMSK cooperative system outperforms a conventional DF scheme in terms of both power and bandwidth efficiency.